The probability of rain on any particular day is 0.2. however, the probability of rain on a day after a rainy day is 0.85, whereas the probability of rain on a day after a non-rainy day is 0.1.
a) on two consecutive days, find the probability of having:
i. two rainy days
ii. exactly one rainy day
iii. at least one dry day
b) on three consecutive days, find the probability of having:
i. three rainy days
ii. exactly one dry day
iii. at most two rainy days

a)

i. = 0.17

ii. = 0.11

iii = 0.83

b)

i. = 0.1445

ii. = 0.0965

iii. = 0.241

step-by-step explanation:

to solve this problem we can represent the probabilities in a probability tree.

where r represents a rainy day and nr represents a day without rain

so, for part a) we have:

observe the attached diagram

then for part b) we have three consecutive days:

observe the attached diagram

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